Unfamiliar partial derivative notation

Question

I've never seen this notation before, so I'm not sure where to start learning about it:

I got it from here: http://neuralnetworksanddeeplearning.com/chap1.html#the_architecture_of_neural_networks (about half way down)

It looks like he's adding two partial derivatives, one for C with respect to v1 and one for C with respect to v2. That makes sense sort of, but why is he multiplying the derivative against the change in v1 and the change in v2.

https://en.wikipedia.org/wiki/Differential_of_a_function#Differentials_in_several_variables — Chappers, Nov 15 '15 at 16:03

score 1 · Accepted Answer · answered Nov 15 '15 at 16:11

1

For a differentiable real valued function of two variables $F(x,y)$, a linear approximation of the change in $F$ when $(x,y)$ moves to $(x+\Delta x,y+\Delta y)$ is given by:

$$\Delta F\approx \frac{\partial F}{\partial x}\Delta x+\frac{\partial F}{\partial y}\Delta y$$

where the partial derivatives are calculated at $(x,y)$. Is it more familiar now?

answered Nov 15 '15 at 16:11

uniquesolution

18,541

Ahhh, linear approximation. Got it. Just saying that the rate of change * change = actual change. Thanks!!! – Blaze Nov 15 '15 at 17:45

Unfamiliar partial derivative notation

1 Answers1